Regularized dequantizer for DCT-based transform coding

ABSTRACT

A new dequantization scheme for DCT-based transform coding, such as JPEG, MPEG and H.26×, is disclosed. The new approach drastically reduces blocking artifacts without smoothing the decoded image. Most discrete cosine transform (DCT) based video coding suffers from blocking artifacts where boundaries of 8×8 DCT blocks become visible on decoded images. The blocking artifacts become more prominent as the bit rate is lowered. In the present invention, a new dequantization technique is disclosed for discrete cosine transform (DCT) based encoding to sharply reduce the blocking artifacts. The dequantization scheme of the present invention sharply reduces blocking artifacts in decoded images through regularization. The performance comparison with the standard JPEG as well as MPEG and H.26×decoding shows visual improvements as well as numerical improvements in terms of the peak-signal-to-noise ratio (PSNR) and the blockiness measure (BM) to be defined.

BACKGROUND OF THE INVENTION

[0001] 1. Technical Field

[0002] This invention relates to digital images including video. Morespecifically, this invention relates to a dequantizer used for decodingof digital images and video compressed by a DCT-based (discrete cosinetransform) transform coding, such as JPEG, MPEG and H.26×.

[0003] 2. Description of the Related Art

[0004] Emergence of Internet video as well as high definitiontelevision, not to mention the literally millions of digital imagescurrently available on Internet, has been fueling the recent surge ofinterest in compression of digital images. In particular, internationalstandards such as JPEG, MPEG and H.26×, for compression of digitalimages and video have received much attention due to the fact that theyare open standards for any developers.

[0005] Image (and video) compression is implemented in an encoder forencoding images using a quantization matrix. The decoder then is able todecode the image, also by using a quantization matrix. In theconventional art, the enconder and the decoder use the same quantizationmatrix. Recently, however, algorithms have been suggested, where theencoder uses one quantization matrix and the decoder uses a differentquantization matrix. The new quantization matrix, used during decoding,is computed (by the encoder) using an approach similar to Miller's leastsquares solution as disclosed in Miller K., “Least squares methods forill-posed problems with a prescribed bound”, SIAM J. Math. Anal., vol.1, pp. 52-74, Feb. 1970 for image restoration applications.

[0006] Another solution is disclosed in Philips W., “Correction to 'JPEGdequantization array for regularized decompression”, IEEE Trans. onImage Proc., vol. 6, no. 6, pp. 883-888, 1997, which offers adequantization scheme different from the standard method.

[0007] Konstantinides, et al. propose yet another technique forcomputing a modified quantization matrix for image sharpeningapplications directly in DCT domain. See Konstantinides K. Bhaskaran V.and Beretta G., “Image sharpening in the JPEG domain”, IEEE Trans. onImage Proc., vol. 8, no. 6, June 1999.

[0008] However, neither approaches guarantee that the dequantizationprocess will map the quantized DCT coefficients to its value±(quantizerspacing/2) in DCT domain. As a result, a smooth recovery is notpossible, especially for compressed images at a low bit-rate.

[0009] Therefore, there is a need for a new dequantizer that can recoverthe original image in a smooth manner.

SUMMARY OF THE INVENTION

[0010] It is an object of the present invention to provide a dequantizerthat recovers the original image in a smooth manner.

[0011] Another object of the present invention is to provide adequantizer that guarantee mapping of quantized DCT coefficients towithin±(quantizer spacing/2).

[0012] The foregoing and other objectives are accomplished by aregularized dequantizer of the present invention. An improved decoder isdisclosed, which can work with the standard MPEG and H.26×compressedvideo as well as JPEG compressed digital images. The dequantizer of thepresent invention is superior over the currently specifieddequantization scheme.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] FIGS. 1(a) and (b) are block diagrams of DCT-based image encoderand decoder of the present invention, respectively.

[0014]FIG. 2 is a flow chart of the software implementing the presentinvention.

[0015] FIGS. 3(a), 3(b) are plots showing PSNR and BM values for atypical I-frame; FIGS. 2(c) and 2(d) for a P-frame; and FIGS. 2(e) and2(f) for a B-frame, all obtained in two iterations.

[0016]FIG. 4(a), 4(b) and 4(c) are an original image (left), the imageas decoded by the standard MPEG (center) and the image as decoded by thedequantizer of the present invention for I-, P- and B-frames,respectively.

[0017] FIGS. 5(a) and (b) are plots of the PSNR and the BM values asfunctions of the quantization scale factor (QUANT of H.263+) using thestandard Lenna image.

[0018] FIGS. 6(a), 6(b), and 6(c) are the image as decoded by H.263+,the image as decoded by the H.263+decompression followed by thedeblocking filter, the image as decoded by the decoded image by theregularized dequantizer of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0019] Modeling DCT-based Transform Coding

[0020] Before describing the details of the regularized dequantizationof the present invention, the conventional DCT-based transform codingcurrently specified in the MPEG standard (as well as JPEG, H.261 andH.263) is reviewed to establish the notation.

[0021] In MPEG or other conventional DCT-based transform codingstandards, the image is first divided into 8×8 blocks and the individualblocks are transformed by the discrete cosine transform (DCT). Theoutput of this operation is denoted by Df, where f is thelexicographically ordered image and the operator D is the appropriatelydefined 2-D DCT matrix. The DCT coefficients are then quantized with orwithout a dead-zone. Since the quantization process includes a division(or a multiplication by its inverse) step by elements of thequantization matrix, the quantization operator Q can be mathematicallyexpressed as follows:

Q{Df}=round {M ⁻¹ Df−sgn(Df)δ/2}=M ⁻¹ Df−sgn{Df}δ/2+½−rem{M ⁻¹Df−sgn(Df)δ/2+½}  (1)

[0022] where round{} and rem{} operators indicate the usual rounding andremainder operations, respectively; and sgn{} is the signum functionthat maps positive, zero and negative valued reals to 1, 0 and −1,respectively. Furthermore, M is a diagonal matrix whose elements consistof appropriately ordered elements of the quantization matrix. Note thatδ=1 for quantization with a dead-zone. If δ=0, Eq. (1) then representsquantization without a dead-zone. Lastly, the identity is also used:

round{x}=x+½−rem+x+½}  (2)

[0023] The quantized DCT coefficients are then encoded losslessly.

[0024] Upon receipt of losslessly encoded quantized DCT coefficients,the decoder first reverses the lossless encoding process to obtainquantized DCT coefficients. The lossless encoding and decoding stepstogether form a mathematical identity. The decoder has access toquantized DCT coefficients Q{Df} as computed by the encoder. Thedequantization operation P can simply be modeled by a multiplication byM, quantization scales followed by a correction for dead-zones. That is,

P{Q{Df}}=M(Q{Df}+sgn{Df}δ/2)=Df+M(½−rem{M ⁻¹ Df−sgn{Df}δ/2+½  (3)

[0025] Again, in the above, δ=1 indicates quantization with a dead-zoneand δ=0 without a dead-zone.

[0026] The conventional decoder then takes the dequantized DCTcoefficients and performs the 2-D inverse discrete cosine transform(IDCT) as follows:

g=D ¹ PQ{Df}=f+D ⁻¹ M(½−rem{M ⁻¹ Df−sgn(Df)δ/2+½  (4)

[0027] Note that what is desired is the original image f; however, theimage as determined by the conventional decoder is g. Thisconventionally decoded image includes the quantization error whichprecisely is the second term of Eq. (4):

error=D ⁻¹ M(½rem{M ⁻¹ Df−sgn(Df)δ/2+½})   (5)

[0028] It is important to note that the quantization error originallyintroduced in the DCT domain (by the rounding operation of Eq. (1), hasbeen re-expressed in the spatial domain. In other words, Eq. (5) isexactly the quantization error expressed in the spatial domain.

[0029] Direct interpretation of the derivation leading to Eq. (5)results in the following. The quantization error as shown in Eq. (5)above is due to the quantization Q followed by the conventionaldequantization described by Eq. (3).

[0030] The present invention is based on finding a better dequantizerusing regularization. Through regularization, with the assumption thatthe image f is smooth, a different dequantization procedure isdeveloped.

[0031] In view of the inequality

−½<½−rem(x+½)≦½  (6)

[0032] The error in the DCT coefficients Oust before the IDCT step) alsoobey $\begin{matrix}{\left| {e_{n}^{\prime}M\left\{ {{1/2} - {{rem}\left( {{M^{- 1}{Df}} - {{{sgn}({Df})}{\delta/2}} + {1/2}} \right)}} \right\}} \middle| {\leq \frac{e_{n}^{\prime}{Me}_{n}}{2}} \right.,{{for}\quad {all}\quad n}} & (7)\end{matrix}$

[0033] where T indicates transpose and e_(η) is the Euclidean basisvector with a “1” in the nth row and zeros in other rows. Although Eq.(7) appears to be cumbersome, what it states is simply that, the errorintroduced (in DCT domain) by the quantizer is limited between+(quantizer spacing/2) for nth DCT coefficient. This observation allowsa slightly different relationship between g and f. For this purpose,define: $\begin{matrix}{c_{ij} = {{2D} - {{IDCT}\quad {of}\quad \left\{ \begin{bmatrix}0 & \Lambda & 0 & 0 & 0 & \Lambda & 0 \\M & \quad & M & M & M & \quad & M \\M & \quad & 0 & 0 & 0 & \quad & M \\0 & \Lambda & 0 & q_{ij} & 0 & \Lambda & 0 \\M & \quad & 0 & 0 & 0 & \quad & M \\M & \quad & M & M & M & \quad & M \\0 & \Lambda & 0 & 0 & 0 & \Lambda & 0\end{bmatrix} \right\}}}} & (8)\end{matrix}$

[0034] where q_(η) is the ijth element of the quantization matrix.Furthermore, let c_(η) be lexicographically ordered version of c_(η).Then, $\begin{matrix}{{g(k)} = {{f(k)} + {\sum\limits_{0 \leq {ij} \leq 1}{{\alpha_{ij}(k)}c_{ij}}}}} & (9)\end{matrix}$

[0035] where the argument (k) indicates the extraction of thecorresponding kth 8×8 block. Thus, all vectors in Eq. (9) are of thesize 64×1. Furthermore, due to the inequality as shown by Eq. (7), thecoefficients α_(η)(k) are restricted to lie within the interval (−½,½].Note that Eq. (9) is satisfied for all 8×8 blocks of the image. This istrue whether or not the dead-zone is used by the quantizer.

[0036] The following observations may be made regarding the matrixc_(η). Firstly, it is precisely the ij^(th) basis vector for the inverseDCT. Secondly, it is the quantization error introduced by the ij^(th)DCT coefficient represented in the spatial domain. In other words, thequantization error introduced by the ij^(th) DCT coefficient manifestsitself as a spatially varying error (except for the DC coefficient whereit would cause a constant error within the 8×8 block) represented byc_(η).

[0037] Regularization

[0038] In view of the previous analysis, the task is: find α_(η)(κ) tominimize ||f−g||₂, the L₂-norm, using Eq. (9). The problem as stated isan ill-posed problem, and a unique solution cannot be obtained. Theremedy is to regularize the problem. By assuming that the original imageƒ(x, y) is “smooth”, find ƒ that minimizes: $\begin{matrix}\left. ||{f - g}\mathop{\text{||}}_{2}^{2}{+ \lambda}||{\nabla f}||_{2}^{2} \right. & (10)\end{matrix}$

[0039] The minimizer of the functional in Eq. (10) obeys the followingEuler-Lagrange Equation: $\begin{matrix}{{F_{f} - {\frac{\partial}{\partial x}F_{f}}},{{- \frac{\partial}{\partial y}}F_{f}},{= 0}} & (11)\end{matrix}$

[0040] where F=(ƒ−g)²+λ)(ƒ_(x) ²+ƒ_(y) ²) and subscripts indicatepartial differentiation along the direction of the subscriptingvariable. Substitution of appropriate variables into the Euler-LagrangeEquation (11) results in the following Poisson Equation: $\begin{matrix}{{\nabla^{2}f} = {\frac{1}{\lambda}\left( {f - g} \right)}} & (12)\end{matrix}$

[0041] with an appropriate boundary condition (Dirichlet or Neumann)depending on the particular application.

[0042] Image Decoding by Regularized Dequantizer

[0043] The decoded image must still be based on the received quantizedDCT coefficients and thus must satisfy Eq. (9). Therefore, Eq. (12)cannot be used by itself. Because a dequantizer is desired that modifiesquantized DCT coefficients by ±(quantizer spacing/2), Eq. (12) must beused together with Eq. (9).

[0044] The substitution of Eq. (9) into a lexicographically orderedversion of Eq. (12) yields: $\begin{matrix}{{\sum\limits_{{0 \leq i},{j \leq 7}}{{\alpha_{ij}(k)}\left( {{Lc}_{ij} - {\frac{1}{\lambda}c_{ij}}} \right)}} = {{Lg}(k)}} & (13)\end{matrix}$

[0045] where L is the matrix representation of the Laplacian operatorfor lexicographically ordered operands (i.e., vectors). Note that theoriginal image f has been completely eliminated in Eq. (13). In fact,all terms that appear in Eq. (13) are known except for the coefficientsα_(y)(κ). Therefore, the problem at hand is to determine α_(η)(κ), usingEq. (13). For this purpose, Eq. (13) may be written in matrix-vectorform as follows: $\begin{matrix}{{\left\lbrack {{Lc}_{00} - {\frac{1}{\lambda}c_{00}}} \middle| \Lambda \middle| {{Lc}_{77} - {\frac{1}{\lambda}c_{77}}} \right\rbrack {á(k)}} = {{Lg}(k)}} & (14)\end{matrix}$

[0046] where á(κ) is the lexicographically ordered version of thecoefficients α_(η)(κ). It can be shown that the system of equationsabove is invertible and it may be solved exactly and á(k) can be foundsimply by inverting Eq. (14). Certain fast FFT-like approaches may alsobe used. Note that Eq. (14) must be satisfied for all 8×8 blocks. Onceá(κ) has been determined for all blocks, the desired image can beobtained by Eq. (9) for all 8×8 blocks. However, because thecoefficients α₇₂ (κ) must be limited to lie in the interval (−½,½], aniterative approach is used. In other words, if any of the computedcoefficients α_(η)(κ) lies outside the interval (−½,½], thosecoefficients must be clipped.

[0047] The algorithm then recomputes the coefficients based on thecurrently available data. The iterative decompression algorithm of thepresent invention implementing the regularized dequantizer is summarizedbelow:

[0048] Initialize image with the conventionally decoded image: f^((o))=g

[0049] Initialize coefficients for all 8×8 blocks: α_(η)(κ)=0

[0050] Loop for m=0,1,2,3,K

[0051] Find the incremental coefficient α_(ij)^((m))(k):

[0052] Solve Eq. (14) with g=f^((m)).

[0053] Update and clip the effective coefficient:a_(ij)(k) = min (max (α_(ij)(k) + α_(ij)^((m))(k), −1/2), 1/2)

[0054] Update the current image (for all 8×8 blocks):${f^{({m + 1})}(k)} = {{g(k)} - {\sum\limits_{{0 \leq i},{j \leq 7}}{{\alpha_{ij}(k)}c_{ij}}}}$

[0055] The end result or the decoded image, is in effect, the IDCT ofthe regularized dequantizer output. In practice, the coefficientsα_(η)(κ) corresponding to low frequency components rapidly grow tovalues outside the interval (−½,½], which is then clipped within theiteration loop. This clipping allows coefficients corresponding tohigher frequency components to rise. In any case, because the finaldecoded image is based on Eq. (13), the present invention guarantees theupdating of received DCT coefficients to within±(quantizer spacing/2)for all DCT coefficients.

[0056] The method described above is a new dequantization scheme incomparison to other approaches described in various DCT-based codingstandards, where the computed DCT coefficients are quantized accordingto the quantizer spacing specified by the quantization matrix elements.As an instance, on the encoder side, suppose

[0057] computed DCT coefficient=41.2

[0058] quantization matrix element for this particular coefficient=8

[0059] encoded data=5 (=round {41.2/ 8})

[0060] Then, on the decoder side,

[0061] received data=5

[0062] quantization matrix element for this particular coefficient=8

[0063] reconstructed DCT coefficient=40=5 * 8

[0064] Note that in this particular case, the quantization error=1.2which is bounded to within ±(quantizer spacing/2). The method of thepresent invention does not simply multiply the quantizer spacing to thereceived data, which in this case is 40. The dequantizer of the presentinvention will map the received data to within the range (36, 44), wherethe actual value is chosen so that the final decompressed image is“smooth” in the sense of minimizing the cost functional given in Eq.(10).

[0065] Implementation

[0066] FIGS. 1(a) and (b) show block diagrams of a DCT-based imageencoder and a decoder of the present invention, respectively. Thepresent invention replaces the two modules within the dark dotted box ofthe decoder shown in FIG. 1(b). The encoder 10, shown in FIG. 1(a),takes the raw image, which are transformed by a DCT module 11 andquantized by a qunatizer 12. The output Q{Df} is then losslessly encodedby the variable length coder (VLC) 13 and trasnsmitted (or stored). Themotion prediction, within the lightly dotted box 14, is only performedfor video. For still images, the motion prediction and all connectionsto it can be discarded. Even for video (MPEG and H.26×) the motionprediction is performed for only P and B-frames.

[0067] The decoder 20, shown in FIG. 1(b), takes the encoded image andreverses the encoding process: variable length decoding (VLD) 21,dequantization by a regularized dequantier 22 of the present inventionfollowed by the IDCT module 23. As for the encoder, the motioncompensation modules shown within the lightly dotted box 24 is notperformed for still images and certain frames of video (I-frames of MPEGand H.26×).

[0068]FIG. 2 shows a flow chart of the software implementing the presentinvention. Step (101) initializes and sets up various parameters andarrays for operations to follows. Namely, in connection to thepreviously described mathematical symbols, the initialization can besummarized as:

[0069] Initialize the image buffer with the conventionally decodedimage: f^((o))=g

[0070] Initialize coefficients for all 8×8 blocks: α₇₂(κ)=0

[0071] Initialize loop count

[0072] Step (102) computes the incremental coefficient α_(ij)^((m))(k)

[0073] for the image update. Step (103) updates and clips the effectivecoefficient, namely it performs the operationα_(ij)(k) = min   (max (α_(ij)(k) + α_(ij)^((m))(k), −1/2), 1/2).

[0074] Step (104) finally updates the current image buffer using theequation:${f^{({m + 1})}(k)} = {{g(k)} - {\sum\limits_{{0 \leq i},{j \leq 7}}{{\alpha_{ij}(k)}c_{ij}}}}$

[0075] Step (105) updates the loop count and Step (106) checks the loopcount to check whether to continue. When loops are no longer necessary,the processing is terminated.

RESULTS

[0076] The performance of the regularized dequantizer of the presentinvention is evaluated and compared to the standard H.263+ with itsstandard quantization table with and without the deblocking filter. Theblockiness measure (BM) defined by the following will be used to comparethe two approaches. $\begin{matrix}{{BM} = {10\quad \log_{10}\left\{ \frac{{\sum\limits_{vertical}{{\frac{\partial\quad}{\partial x}\left( {f - \hat{f}} \right)}}_{2}^{2}} + {\sum\limits_{horizontal}{{\frac{\partial\quad}{\partial y}\left( {f - \hat{f}} \right)}}_{2}^{2}}}{N_{pix}} \right\}}} & (15)\end{matrix}$

[0077] where N_(pix) is the total number of pixels summed. In the above,ƒ is the original image and ƒ is the decompressed image by one of (i)MPEG, (ii) H.263+ decompression, (iii) H.263+ with its deblocking filterand (iv) the regularized dequantizer of the present invention. Note thatthe differences in the derivatives across the 8×8 block boundary aresummed only along vertical and horizontal block boundaries. Higher BMindicates more severe blocking artifact.

[0078] FIGS. 3(a) and (b) show PSNR and BM values for a typical I-frame;(c) and (d) for a P-frame; and (e) and (f) for a B-frame, all obtainedin two iterations. Note that the improvement provided by the regularizeddequantizer of the present invention for I frame is much greater thanthat of the P- and B-frames. Although improvements in actual PSNR valuesappear to be small (less than 1 dB for I-frame and almost negligible forB-frame) the improvements in BM values are more apparent for all frametypes, especially for I-frame. In addition, a few trends can be observedfrom these plots. (1) The performance difference is most obvious for theI-frame and this difference is less prominent the P- and the B-frames.(2) The improvement in both the PSNR as well as BM becomes more relevantfor low bit rates. (3) The improvement in the BM is greater than that ofthe improvement in PSNR for all frame types. (4) Higher performance gaincan be expected for lower bit rate videos, however for extremely highbit rate videos, the performance gain will not be as obvious.

[0079] In addition to the numerical improvements discussed above, thevisual improvement offered by the regularized dequantizer of the presentinvention becomes apparent upon viewing the zoomed decompressed images.

[0080]FIG. 4 shows the original image (left), the image as decoded bythe standard MPEG (center) and the image as decoded by the dequantizerof the present invention. FIGS. 4(a), (b) and (c) show the three imagesfor I-, P- and B-frames, respectively. All images are zoomed by a factortwo. The visual improvement offered by the regularized dequantization isself-evident upon a quick comparison of these images, with the largestimprovement seen for the I-frame.

[0081] The present invention is also applicable to H.26x videocompression standard as the standard is also based on DCT transformcoding. In particular, focus on the most recent H.263+ standard. Theperformance of the regularized dequantizer of the present invention isevaluated and compared to the standard H.263+ with its standardquantization table with and without the deblocking filter.

[0082]FIG. 5 shows plots of the PSNR (a) and the BM (b) values asfunctions of the quantization scale factor (QUANT of H.263+) using thestandard Lenna image. The present invention consistently provides higherPSNR and lower BM values for all values of QUANT. The readilyrecognizable trend is that larger the quantization step size (QUANT) andthus lower the bit-rate, higher the performance gain of the regularizeddequantizer over the conventional dequantizer. All images were obtained(for the regularized approach) in two iterations.

[0083] As was the case for MPEG video shown previously, althoughimprovements in actual PSNR values appear to be small (less than 1 dB),the visual improvement offered by the regularized dequantizer of thepresent invention becomes apparent upon viewing the zoomed images.

[0084]FIG. 6(a) shows the image as decoded by H.263+; FIG. 6(b) showsthe H.263+ decompression followed by the deblocking filter; FIG. 6(c)shows the decoded image by the regularized dequantizer of the presentinvention. All images are zoomed by a factor three. Again, the visualimprovement offered by the regularized dequantization is self-evidentupon a quick comparison of these images.

[0085] To summarize, the present invention consistently provides higherPSNR and lower BM values for all values of the bit rate. The readilyrecognizable trend is that lower the bit rate, higher the performancegain achieved by the regularized dequantizer of the present inventionover the conventional decompression. A new method is presented fordecompressing DCT-encoded images based on the regularized dequantizer ofthe present invention. The superiority of the present invention has beendemonstrated over the existing MPEG as well as H.263+ standard with andwithout its deblocking filter. As simulations have indicated, thepresent invention would be particularly appropriate for low-bit ratevideos.

[0086] While the invention has been described with reference topreferred embodiments, it is not intended to be limited to thoseembodiments. It will be appreciated by those of ordinary skilled in theart that many modifications can be made to the structure and form of thedescribed embodiments without departing from the spirit and scope ofthis invention.

What is claimed is:
 1. A dequantizer for reconstructing originaltransform cofficients from quantized transform coefficients from anoriginal, decompressed image, comprising: means for receiving thequantized transform coefficients; and means for reconstructing thedequantized transform coefficients from the received quantized transformcoefficients by selecting transform coefficients that minimizes a costfunction indicating a smoothness of the original decompressed image. 2.The dequantizer of claim 1, wherein said quantized transformcoefficients are DCT transform coefficients.
 3. The dequantizer of claim2, wherein the quantized DCT coefficients are mapped to originaldequantized coefficients where a quantization error is boundwithin±(quantizer spacing/2).
 4. A method of reconstructing originaltransform cofficients from quantized transform coefficients from anoriginal, decompressed image, comprising the steps of: receiving thequantized transform coefficients; and reconstructing the dequantizedtransform coefficients from the received quantized transformcoefficients by selecting transform coefficients that minimizes a costfunction indicating a smoothness of the original decompressed image. 5.The method of claim 4, wherein said quantized transform coefficients areDCT transform coefficients.
 6. The method of claim 5, wherein thequantized DCT coefficients are mapped to original dequantizedcoefficients where a quantization error is bound within±(quantizerspacing/2).
 7. A video decoder for decoding an encoded video containingtransform coefficients representing an original video, comprising:decoder means for decoding the encoded video to extract quantizedtransform coefficients; dequantizer means for converting the quantizedtransform coefficients into dequantized transform coefficients, andinverse-transform means for converting the dequantized transformcoefficients into the original image.
 8. The video decoder of claim 7,wherein said dequantizer means comprises: means for receiving thequantized transform coefficients; and means for reconstructingdequantized transform coefficients from the quantized transformcoefficients by selecting transform coefficients that minimize a costfunction indicating a smoothness of the original decompressed image. 9.The video decoder of claim 8, wherein the transform coefficients are DCTtransform coefficients.
 10. The video decoder of claim 9, wherein theoriginal image is part of a video decoded using the MPEG relatedstandard.
 11. The video decoder of claim 9, wherein the original imageis part of a video decoded using the H263 related standard.
 12. A methodof decoding an encoded video containing transform coefficientsrepresenting an original video, comprising the steps of: decoding theencoded video to extract quantized transform coefficients; convertingthe quantized transform coefficients into dequantized transformcoefficients, and converting the dequantized transform coefficients intothe original image.
 13. The method of claim 12, wherein the step ofconverting the quantized transform coefficients into dequantizedtransform coefficients comprises the steps of: receiving the quantizedtransform coefficients; and reconstructing dequantized transformcoefficients from the quantized transform coefficients by selectingtransform coefficients that minimize a cost function indicating asmoothness of the original decompressed image.
 14. The method of claim13, wherein the transform coefficients are DCT transform coefficients.15. The method of claim 14, wherein the original image is part of avideo decoded using the MPEG related standard.
 16. The method of claim14, wherein the original image is part of a video decoded using the H263related standard.